A stock is currently trading at $50. A three-month at-the-money European put option on the stock costs 2.178. The delta of the put is $- 0.4355$ and the gamma of the put is 0.063. Given these values, if the stock price decreases by $5.00, then the best estimate for the new value of the put is
A) $4.35$ .
B) $5.14$ .
C) $0.79$ .
D) $3.57$ .
E) Zero.

Question

Quizplus · Accepted Answer

The new value of the put can be estimated using the delta and gamma of the option. The change in the option's price due to a $5 decrease in the stock price can be calculated as: Change in price = Delta * Change in stock price + 0.5 * Gamma * (Change in stock price)^2 = (-0.4355) * (-5) + 0.5 * 0.063 * (-5)^2 = 2.1775 + 0.7875 = 2.965. Adding this to the original price of the put option gives: 2.178 + 2.965 = 5.143. Therefore, the best estimate for the new value of the put is approximately $5.14.

A Stock Is Currently Trading at $50 −0.4355- 0.4355−0.4355 And the Gamma of the Put Is 0

A Stock Is Currently Trading at $50 $- 0.4355$ And the Gamma of the Put Is 0